Geodesic
The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in~$L_1$ equal to zero on a~given set
Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 1-35

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The precise structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere (a.e.) of Fourier series of functions in the class $L_1(T^N)$, $N\geqslant1$, $T^N[0,2\pi]^N$, and vanishing on a given measurable set $E$ is found (in the case $N\geqslant2$ this is done for both rectangular and square summation). Bibliography: 21 titles. 
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     author = {I. L. Bloshanskii},
     title = {The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple {Fourier} series of functions in~$L_1$ equal to zero on a~given set},
     journal = {Izvestiya. Mathematics },
     pages = {1--35},
     publisher = {mathdoc},
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     number = {1},
     year = {1990},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a0/}
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I. L. Bloshanskii. The structure and geometry of maximal sets of convergence and unbounded divergence almost everywhere of multiple Fourier series of functions in~$L_1$ equal to zero on a~given set. Izvestiya. Mathematics , Tome 35 (1990) no. 1, pp. 1-35. http://geodesic.mathdoc.fr/item/IM2_1990_35_1_a0/